This systematized literature review examines how prompt engineering in generative AI (GenAI) has been used to support Project-Based Learning (PjBL) and develops a conceptual framework for Network Programming courses. Following the PRISMA 2020 statement, records published from 2020 to 2026 were retrieved from IEEE Xplore, ScienceDirect, SpringerLink, Google Scholar, and Garuda/Sinta. Of 310 records identified, 242 remained after duplicate removal, 56 were assessed in full text, and 24 studies met the eligibility criteria. Screening decisions were cross-checked by a second reviewer (Cohen's κ = [....]), and study quality was appraised with the Mixed Methods Appraisal Tool (MMAT). Data were analyzed through a hybrid deductive–inductive thematic analysis following Braun and Clarke's six phases: the four research questions served as a priori categories, sub-themes were coded inductively until no new codes emerged, and coding disagreements were resolved by consensus. The results revealed that structured and scaffolded prompting is consistently associated with deeper engagement than unstructured prompting in programming classes, and that GenAI-supported PjBL preserves student autonomy and creativity when AI interaction is embedded in project stages and students must justify their technical decisions. Only one included study addressed computer networking directly. Reported challenges were excessive dependence on AI-produced solutions, shallow learning, and unclear assessment practices. Unlike existing PjBL–GenAI models, which treat AI as a generally available tool, the proposed three-layer framework (competency, scaffolding, and assessment) specifies when and how prompting is taught, constrained, and evaluated across network programming project milestones, and it yields testable propositions for future empirical research.